Exploratory data analysis in the Red wine composition Dataset
Introduction to the dataset:
The Dataset chosen for this project is the red wine composition dataset. I chose this dataset because I am really interrested in wine and i thought it would be really interresting dataset. This dataset comes from Cortez et al. 2009 [1]. It present different caracteristics of red and white wine. Only the Red wine data was explored in this document. This dataset contain 1599 wine analyses. Each sample was analyzed for different characteristics and then the wine quality was assessed by at least 3 expert giving a grade between 0 (very bad) and 10 (very excellent). More informations can be found in the M&M file.
Wine characteristics studied:
The variables present in this dataset are:
- fixed acidity (tartaric acid - g / dm³)
- volatile acidity (acetic acid - g / dm³)
- citric acid (g / dm³)
- residual sugar (g / dm³)
- chlorides (sodium chloride - g / dm³
- free sulfur dioxide (mg / dm³)
- total sulfur dioxide (mg / dm³)
- density (g / cm³)
- pH
- sulphates (potassium sulphate - g / dm3)
- alcohol (% by volume) Output variable (based on sensory data): 12 - quality (score between 0 and 10)
Univariate Plots Section
Lets look at the dataset before plotting anything. Looking at the structure of the dataset gives a good sense of it.
## 'data.frame': 1599 obs. of 13 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : int 5 5 5 6 5 5 5 7 7 5 ...One thing I first notice is that we have 13 variables instead of 12. The unwanted variable is the first one: X. The summary of this variable has been computed below:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.0 400.5 800.0 800.0 1200.0 1599.0In this summary we see that the variable range from 1 to 1599 which is the number of samples analysed in this dataset. To check if this column is just an artefact from a row numbering in our csv file that has been misinterpreted during importation we can compute an histogram of this variable with a binwidth of 1:
We clearly see that each X value has a frequency of 1. We can conclude that this column can be removed from the dataset as it only numbered the sample and doesn’t represent anything.
Another “problem” could be the mapping of quality as an integer and not a factor. Quality is a number representing a qualitative variable. The use of integer type on this variable might be interresting when modeling or doing scatterplot, but it is a bit misleading. I added a column to the dataset named quality.factor to code the quality variable as a factor while keeping the integer mapping in case it is needed later.
Next let’s compute a summary of the dataset:
## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. : 4.60 Min. :0.1200 Min. :0.000 Min. : 0.900
## 1st Qu.: 7.10 1st Qu.:0.3900 1st Qu.:0.090 1st Qu.: 1.900
## Median : 7.90 Median :0.5200 Median :0.260 Median : 2.200
## Mean : 8.32 Mean :0.5278 Mean :0.271 Mean : 2.539
## 3rd Qu.: 9.20 3rd Qu.:0.6400 3rd Qu.:0.420 3rd Qu.: 2.600
## Max. :15.90 Max. :1.5800 Max. :1.000 Max. :15.500
##
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## Min. :0.01200 Min. : 1.00 Min. : 6.00
## 1st Qu.:0.07000 1st Qu.: 7.00 1st Qu.: 22.00
## Median :0.07900 Median :14.00 Median : 38.00
## Mean :0.08747 Mean :15.87 Mean : 46.47
## 3rd Qu.:0.09000 3rd Qu.:21.00 3rd Qu.: 62.00
## Max. :0.61100 Max. :72.00 Max. :289.00
##
## density pH sulphates alcohol
## Min. :0.9901 Min. :2.740 Min. :0.3300 Min. : 8.40
## 1st Qu.:0.9956 1st Qu.:3.210 1st Qu.:0.5500 1st Qu.: 9.50
## Median :0.9968 Median :3.310 Median :0.6200 Median :10.20
## Mean :0.9967 Mean :3.311 Mean :0.6581 Mean :10.42
## 3rd Qu.:0.9978 3rd Qu.:3.400 3rd Qu.:0.7300 3rd Qu.:11.10
## Max. :1.0037 Max. :4.010 Max. :2.0000 Max. :14.90
##
## quality quality.factor
## Min. :3.000 5 :681
## 1st Qu.:5.000 6 :638
## Median :6.000 7 :199
## Mean :5.636 4 : 53
## 3rd Qu.:6.000 8 : 18
## Max. :8.000 3 : 10
## (Other): 0Looking at the repartition of value of the different variables, we can see that fixed.acidity, residual.sugar, chlorides, free.sulfur.dioxide, total.sulfur.dioxide and sulphates shows some really high maximal value compared to the 3rd quartile value. These outlier could be problematic later.
We will now look at the shape of each variable. First I will look at non factor variable. I find Boxplots to be a good way to visualise distribution feature such as quartile and outliers, but they aren’t as detailled as histograms. I will make these two type of plot side by side. To avoid repetition I created a function named distrib that make the plot.
# function to display a boxplot and an histogram side by side.
# input:
# - df: dataframe
# - x1: variable to plot
# - bi: number of bins to use for the histogram
distrib <- function(df = red, x1, bi = 30) {
p1 <- ggplot(data = df, aes_string(x = x1)) +
geom_histogram(bins = bi)
p2 <- ggplot(data = df, aes_string(y = x1))+
geom_boxplot(aes(x = 1))+
stat_summary(aes(x = 1), fun.y = "mean",
geom = "point", color = "red", shape = 3, size = 4)
grid.arrange(p1, p2, ncol = 2)
}distrib(x1 = "fixed.acidity")
fixed acidity show a skewed distribution with a long tail between 12 and 16. Most of the sample have a fixed acidity value between 6 and 10 g/dm³
distrib(x1 = "volatile.acidity")
Volatile acidity also show a long tailled distribution, but with a lot less outliers. Most of the sample have a value of 0.2 to 0.8 g/dm³.
distrib(x1 = "citric.acid")
The citric acid distribution is again skewed, but only shows one outlier. The majotiry of the sample have a concentration of 0 to 0.65 g/dm³. The histogram show that there is lots of wine with a concentration near 0 g/dm³, then the number of sample with a concentration between 0 and 0.25 g/dm³ decrease until 0.25 g/dm³ around the median, we have an increase in the number of sample with such a concentration. There is another high count for sample with citric acid concentration around 0.5g/dm³. It is interresting to see these high count. There might be a biological reason.
distrib(x1 = "residual.sugar")
Residual sugar shows a highly skewed distribution with lots of ponctual extreme values. Most of the variation appear below 4 g/dm³. I will zoom on the part between 1 and 4 g/dm³
ggplot(data = red, aes(x = residual.sugar))+
geom_histogram()+
xlim(1, 4)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 127 rows containing non-finite values (stat_bin).## Warning: Removed 1 rows containing missing values (geom_bar).
Zooming allow us to see that the distribution of resdual sugar is bell shaped between 1.25 and 3 g/dm³. After 3 g/dm³ the number of sample decrese slowly.
distrib(x1 = "chlorides")
The chloride distribution is even more extremly skeawed than residual sugar. I will zoom on the part with chlorides concentration between (0.025 , 0.13) g/dm³.
ggplot(data = red, aes(x = chlorides))+
geom_histogram()+
xlim(0.025, 0.13)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 80 rows containing non-finite values (stat_bin).## Warning: Removed 1 rows containing missing values (geom_bar).
In this range, the data repartition looks gaussian.
distrib(x1 = "free.sulfur.dioxide")
The free sulfur dioxide distribution also sow some outliers, but is much less skewed than the example before.
distrib(x1 = "total.sulfur.dioxide")
The total sulfur dioxide repartition ooks similar to the free sulfur dioxide repartition. But there is 2 outliers with high SO2 concentrations. When we zoom on the part with most of the frequency:
distrib(x1 = "density")
density shows a gaussian type density curve. Most of the sample have a density of (0.993, 1.000) g/dm³.
distrib(x1 = "pH")
The pH also show a gaussian density curve centered in 3.310.
distrib(x1 = "sulphates")
The sulphate distribution show some outliers, most of the values are found below 1-1.20 g/dm³.
distrib(x1 = "alcohol")
alcohol show a skewed distribution.
Looking at thoses variables, we have seen variables with very little variation between the 1st and 3rd quaritle: chlorides, residual sugar and sulphates. The density and pH parameter have a centered distribution while other parameters have in general a distribution skewed toward large value.
The next step is to look at the repartition of wine between the different quality, an histogram is the best way to have an overview.
In this dataset we have wine with quality ranging from 3 to 8. No wine have really bad quality (0 to 2) and no one have really good quality (9, 10). The majority of wine fall into the medium quality, ~80% of the wine were of quality 5 and 6. The quality distribution look balanced in its range, but have more wine with a quality score higher than 6, than quality lower than 5.
Univariate Analysis:
What is the structure of your dataset?
This dataset contain the composition analysis and quality score of 1599 wines. The composition parameters found in this dataset are:
- fixed.acidity
- volatile.acidity
- citric.acid
- residual.sugar
- chlorides
- free.sulfur.dioxide
- total.sulfur.dioxide
- density
- pH
- sulphates
- alcohol
The quality has been recorded as a grade from 0 (very bad) to 10 (very good). Looking at the repartition of wine quality, we have seen that scores lies between 3 and 8 with the majority of wine tested having a medium quality (5-6), and that there is more wine with quality 7 - 8 than quality 3 - 4.
What features of is there in your dataset?
One interresting feature is obviously the quality of the wine as it is the main reason one would drink wine. But looking at the repartition of the different variables some showed a really low variability and it might be difficult to easily find a relationship describing quality. Another interresting part could be to look at the relations between variables. For instance, we have 4 variables related to acidity of the wine:
- fixed.acidity
- volatile.acidity
- citric.acid
- pH
We might be able to find a relation between them. Also it could be interresting to look at relations between free.sulfur.dioxide, total.sulfur.dioxide and sulphates as they are related to SO2 concentration.
Did you create any new variables from existing variables in the dataset?
I just created a factorial version of the quality variable. In other parts of the analysis I might create a new variable accounting for quality with only 4 level:
- bad: qualtity 3 and 4
- medium low: quality 5
- medium high: quality 6
- good: quality 7 and 8
Because wine with low and high quality are not a big part of our sample, it could make some visualisation easier to read. This idea is not fixed yet we will see if it shows any interresting relations compared to the actual quality system.
Bivariate Plots Section
First lets use the ggcorr function to go a bit faster in representing the variables against each other (variables were plotted against each other, but that project will look at linear correlation as a guide to analyse relations between variables):
## Warning in textData$x[1:layout.exp] <- spacer: le nombre d'objets à
## remplacer n'est pas multiple de la taille du remplacement
Looking at the linear correlation coefficient gives us a good idea of linear relationships. I will first talk about relationships that have a linear correlation around |0.5| or better, and then relationship between |0.2| and |0.4|.
The strongest linear correlations are:
- total.sulfur.dioxyde and free.sulfur.dioxyde with a correletion of 0.668 this correlation seems logical as free.sulfur.dioxyde represent a part of total.sulfur.dioxyde.
- citric.acid with fixed.acidity with a correletion of 0.672
- pH with fixed.acidity with a correletion of -0.683
- citric.acid with pH with a correletion of -0.542
- citric.acid with volatile.acidity with a correlation of -0.552
These four correlation are logical as they happen between different acids or between acids and the pH which represent the acidity of the wine. The negative correletion coeficient between pH and other acids comes from the fact that the lower the pH the more acid the solution is.
- density with fixed.acidity with a correletion of 0.668
- density with alcohol with a correletion of -0.496
We know that the desity is know to be related to alcohol and the sugar content (see M&M file), it is therefore not surprising to find a relation between density and alcohol. Despite this relation, the linear relationship between density and residual.sugar is not as strong (corr coef of 0.355) as I would expect it to be. If we plot density against alcohol and residual sugar to see the difference.
pa <- ggplot(data = red, aes(x = alcohol, y = density))+
geom_point()+
geom_smooth(method = "lm", se = FALSE)
pz <- ggplot(data = red, aes(x = residual.sugar, y = density))+
geom_point()+
geom_smooth(method = "lm", se = FALSE)
grid.arrange(pa, pz, nrow = 1)
We already discussed the high number of outliers in the residual sugar variable. On the scaterplot we can see that most of the samples have a residual sugar below the 4 g/dm³.We will remove sample with residual sugar higher than 4 to see if we can have a better correlation. The 4 g/dm³ is an arbitrary value decided after having a look at the distribution of residual sugar, it doesn’t come from a ny statistical method of outlier detection.
lower_rs <- subset(red, residual.sugar <= 4)
co <- cor(lower_rs$density, lower_rs$residual.sugar)
co1 <- sprintf("r = %.3f", round(co, digits = 3))
ggplot(data = lower_rs, aes(x = residual.sugar, y = density))+
geom_point()+
geom_smooth(method = "lm")+
annotate("text", x = 1.25, y = 1.001, label = co1)
By removing the data point for sample with residual sugar over 4 we can see that the correletion coefficient has been slightly improved, but we only improve from r = 0.355 to r = 0.391. We see that values are only found for some specific residual sugar value. It probably comes from the measurment method and the precision of the equipment used that probably round the residual sugar value to the hundredth of gram/dm³.
An interresting relationship is the density and fixed.acidity relationship.
ggplot(data = red, aes(x = fixed.acidity, y= density))+
geom_point()+
geom_smooth(method = 'lm', se = FALSE)
This relationship is interresting as fixed.acidity is in majority formed by the tartric acid which comes from the fruit directly (tartric acid in wine) and not the fermantation, so part of the wine density is a direct result of the grape quality at harvest.
Some of the less pronounced linear relationships tendencies can be found between:
- fixed.acidity and volatile acidity, coeficient of -0.256
- pH and volatile.acidity, coefficient of 0.235
- volatile.acidity and sulphates, coefficient of -0.261
- volatile.acidity and alcohol, coefficient of -0.202
- citric.acid and chlorides, coefficient of 0.204
- citric.acid and density, coefficient of 0.313
- citric.acid and sulphates, coefficient of 0.313
- pH and alcohol, coefficient of 0.206
These coeficients show the tendency of a linear relation between componant of acidity and other characteristics observed in the wine. Other coefficient greater than |0.2| can be found, but as they don’t relate to the acidity charachteristics I decided To let them aside for this report.
Next we should look at the quality variable and its relation to other characteristics. I will first look at relation with quality to see interresting relationships. Once I find interresting relationships, I will explore the boxplot and compare boxplot with 10 quality classes and the boxplot with the 4 quality classes discussed before.
By looking at thoses boxplot, interresting trends are seen for volatile.acidity, citric.acid, alcohol. Other variables show lesser impressive pattern or trend.
First, let’s look at these boxplot, we will also compare them to a boxplot using the 4 class category for quality discussed before.
two_box <- function(df = red, x1 = "quality.factor",
x2 = "quality.four", y) {
p1 <- ggplot(data = df, aes_string(x = x1, y = y))+
geom_boxplot()+
stat_summary(fun.y = "mean",
geom = "point", color = "red", shape = 3, size = 2)
p2 <- ggplot(data = df, aes_string(x = x2, y = y))+
geom_boxplot()+
stat_summary(fun.y = "mean",
geom = "point", color = "red", shape = 3, size = 2)
grid.arrange(p1, p2, nrow = 1)
}
two_box(y = "volatile.acidity")
Volatile acidity show a decrease in acetic acid with wine having a better quality. According to the wikipedia article about acid in wine, acetic acid is produce if the wine as been exposed to oxygen during its fermentation. This acid is associated to vinegar taste which is equivalent to a bad quality and not an enjoyable drink. This article also state that amount over 600mg/l (=0.6g/dm³) are easily detected by most people. It then seems logical that wine expert can qualified wine with acetic acid up to 0.4g/dm³ as they are trained to detect imperfection in wine. We see that a wine of medium quality show in median 0.6g/dm³. Interrestingly, it seems that acetic acid concentraton below 0.4g/dm³ aren’t making any differences as the median and repartition of acetic acid concentration between wine of quality 7 and 8 are similar. volatile acidity also show outliers with high volatile acidity while they have a quality of 8, maybe these wine with high volatile acidity have some other charachteristics that could mask or compensate for it. The boxplot using the 4 quality level only show the decreasing trend. It hide the plateau in concentration between quality 7 and 8.
two_box(y = "citric.acid")
Citric acid shows a positive relatioship, wine with higher concentration seems to be rated with a higher quality. Citric acid is reported adding freshness taste to wine. We see that for quality over 7 the citric acid doesn’t seems to help increase the quality score. The 4 category boxplot doesn’t add much, it is interresting to see the difference between mean and median in low (3-4) quality. Because of the highly skewed distribution of concentration, the mean doesn’t show as much differences as the median.
two_box(y = "alcohol")
The alcohol relationship to quality is really interresting because wine with quality between 3 and 5 have a similar median of alcohol concentration, but wine with quality over 5 it appears that higher alcohol concentration is correlated with higher quality score. Again, using only 4 quality level doesn’t add to the interpretation, but it could help modelise relations because category with low sample number would have more sample and thus could help have stronger statistical meaning.
Another interresting fact is the range and number of outlier found for a lot of variables. For example residual sugar:
p1 <- ggplot(data = red, aes(x = quality.factor, y = residual.sugar))+
geom_boxplot()+
stat_summary(fun.y = "mean",
geom = "point", shape = 3, color = "red")+
ggtitle("with outliers")
p2 <- ggplot(data = subset(red, red$residual.sugar <= 4), aes(x = quality.factor, y = residual.sugar))+
geom_boxplot()+
stat_summary(fun.y = "mean",
geom = "point", shape = 3, color = "red")+
ggtitle("without residual sugar > 4g/dm³")
grid.arrange(p1, p2, nrow = 1)
We see that by removing extreme value, we have a better view of the repartition of the residual sugar variable, but in the case of residual sugar it doesn’t help us find any trend. The fact that residual sugar show so many outliers could be explained because there is different style of wine and in each category quality is defined a bit differently. Wine tasting is a complicated task and quality of a wine depend on the different general quality, but is also dependend on a wide array of chemicals changing its taste.
By reducing the number of category for the quality variable we aren’t showing trend that where hidden, but we have group containing more sample, this can give a better statistical weight to each category feature.
Multivariate Plots Section
To start with multivariate plotting, I first want to look at relation between pH and citric acid because of its corelation coefficient, and color the point by the volatile acidity.
This first graph show a decreasing relationship between citric acid and pH, but also that for the same pH the more citric acid, the less volatile acidity. It seems logical as pH comes from the acidity of every acid found in the wine.
Next I want to see the combination of volatile acidity and citric acid over the different quality of wine.
In this graph we see the volatile acidity and the citric acid, looking at the color gradient and the regression lines, we can see that high quality wine have a lower volatile acidity content, we also see that volatile acidity and citric acid share a decreasing relationship, the more citric acid, the less volatile acidity in the wine.
In the next graph I will look at the relation found in the first graph, but facet it by quality score.
In this graph we see that within each quality score the whole range of volatile acidity and citric acid can be found. Another interresting remark is the differences in number between the middle category (quality = 5-6) and the other category. Another interesting fact in this dataset is that category with lower wine number have a gap between wine with citric acid concentration lower than 0.125g/dm³ and higher than 0.20-0.25g/dm³. Let’s try to look at the same graph but faceted following the aggregation of lower quality and higher quality wine.
With these category having higher number of wine we see the separation into groups more easily. In the high and low quality groups these two groups are separate. I have no interpretation of this observation.
Next lets look at the fixed acidity, pH and citric acid at the same time.
ggplot(data = red, aes(x = pH, y = fixed.acidity, color = citric.acid))+
geom_point(position = position_jitter())+
facet_wrap(~quality)+
scale_colour_gradientn(colours = rainbow(3))
We can see the positive correlation between fixed.acidity and citric acid found before. Fixed acidity is the measure of Tartric acid. This acid is considered one of the most important in wine. Looking at the repartition of tartric acid within the pH range, it is definitely an important factor in acidity of the wine.
As reported in the wikipedia article, tartric acid and citric acid comes from the grapes composition, it could be interresting to have information on the variety used to produce the wine tested. The soil composition also has an impact on grape composition, the soil informations could also give interresting insight on the relation between wine acids.
Next I will try to see the repartition of residual sugar and alcohol by category. Residual sugar being related to the alcohol fermentation and the inithial sugar content we could see interresting trend, even if no linear trend should be found (see correlations).
I chose to plot the four quality category, and display the original quality category with color. In these visualisation, we see that residual sugar and alcohol doesn’t have any relation.
If we look at the relation between alcohol and quality, we can see that the range of alcohol is wider for wine wit high and medium high quality.
Next We could try to see if linear regression could provide a way to modelise the quality of a wine using the different variable. After seeing the relations between quality and the different variable not showing clear trend or showing non linear tendency we shouldn’t expect too much, but it could be interresting to see such a model, also we could compare the full model with model using only alcohol, and model using some or all the acid related variable.
##
## Calls:
## m1: lm(formula = quality ~ volatile.acidity, data = red)
## m2: lm(formula = quality ~ volatile.acidity + citric.acid, data = red)
## m3: lm(formula = quality ~ volatile.acidity + citric.acid + fixed.acidity,
## data = red)
## m4: lm(formula = quality ~ volatile.acidity + citric.acid + fixed.acidity +
## pH, data = red)
## m5: lm(formula = quality ~ alcohol, data = red)
## m6: lm(formula = quality ~ fixed.acidity + volatile.acidity + citric.acid +
## residual.sugar + chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol, data = red)
##
## ===========================================================================================
## m1 m2 m3 m4 m5 m6
## -------------------------------------------------------------------------------------------
## (Intercept) 6.566*** 6.529*** 6.450*** 4.573*** 1.875*** 21.965
## (0.058) (0.089) (0.121) (0.640) (0.175) (21.195)
## volatile.acidity -1.761*** -1.723*** -1.746*** -1.747*** -1.084***
## (0.104) (0.125) (0.127) (0.127) (0.121)
## citric.acid 0.063 -0.032 0.027 -0.183
## (0.115) (0.152) (0.153) (0.147)
## fixed.acidity 0.014 0.040* 0.025
## (0.015) (0.017) (0.026)
## pH 0.498** -0.414*
## (0.167) (0.192)
## alcohol 0.361*** 0.276***
## (0.017) (0.026)
## residual.sugar 0.016
## (0.015)
## chlorides -1.874***
## (0.419)
## free.sulfur.dioxide 0.004*
## (0.002)
## total.sulfur.dioxide -0.003***
## (0.001)
## density -17.881
## (21.633)
## sulphates 0.916***
## (0.114)
## -------------------------------------------------------------------------------------------
## R-squared 0.153 0.153 0.153 0.158 0.227 0.361
## adj. R-squared 0.152 0.152 0.152 0.156 0.226 0.356
## sigma 0.744 0.744 0.744 0.742 0.710 0.648
## F 287.444 143.812 96.170 74.719 468.267 81.348
## p 0.000 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -1794.312 -1794.160 -1793.707 -1789.240 -1721.057 -1569.138
## Deviance 883.198 883.030 882.530 877.612 805.870 666.411
## AIC 3594.624 3596.320 3597.415 3590.479 3448.114 3164.277
## BIC 3610.756 3617.828 3624.300 3622.742 3464.245 3234.179
## N 1599 1599 1599 1599 1599 1599
## ===========================================================================================The first remark is that all these models show low R squared (0.153 to 3.61). So these models are not really good, the variables account for less than 1/2 of the variance in quality. I will next compare the model with only acid related variables (models m1-m4), then look at the last two models.
Looking at the acids models, we observe no difference in R^2 between model using volatile acidity, fixed acidity and citric acid. We also see that in the first three models volatile acidity is the only significant variable. In the third model pH add a small improvement in R^2 but it is really minimal. This can be explained by looking at the graph showed before and that acid parameters show some relations. These variables aren’t showing linear trend with quality and they seem to be higly related to each other. This lack of independence makes the added information coming from one of these variable inferable from the result of one of the other variables.
We already saw that alcohol showed an interresting trend with quality, the model m5 show a R^2 higher than the one from the alcohol data. In this model alcohol account for 22% of the variance in quality.
In the complete model we see that the created model account for only 36% of the variance in quality. In this model, the variable showing the most significance are:
- volatile acidity
- alcohol
- chlorides
- total.sulfur.dioxide
- sulphates
Final Plots and Summary
Plot One
Description One
This boxplot show the interresting relation between alcohol and quality. The positive relationship between alcohol and quality for wine with quality over 5 is the reason it is a significant factor in the linear regression we did before. I added the sample in the background to show the repartition of sample within category. We observe the high number of sample falling into the 5-6 quality category. Category 5-6 account for 80% of the data points.
Plot Two
Description Two
This scatter plot present the volatile acidity and the citric acid per quality. We see the negative relatioship between volatile acidity and citric acid found with the negative correlation coefficient (r = -0.552) to be true for every category, each regression line being decreasing. It means that for higher volatile acidity level, we have lower citric acid concentration. Looking at the quality regression line, and point color, we observe that for lower quality wine tend to contain more volatile acidity.
The strong linear correletion coefficient show that citric acid and colatile acidity are not independent variables. This dependent relationship between acid are part of the explaination for having only two of these variable significant in our linear modelisation.
Plot Three
Description Three
We see again the relation between some of the acid variables. We can see the positive relationship between citric acid and tartric acid (= fixed acidity) (r = 0.672), and their relation to pH. fixed acidity has a decreasing relationship to ph (r = -0.683). pH also have a decreasing relationship with citric acid (r = -0.542). These relationship are decreasing because pH scale is lower when the acidity increases.
Looking at the different quality facet, we see similar pattern.
Reflection
I looked at the composition of wine and the repartition of chemical composition within different wine. We also compared the quality of wine and tried to do a simple linear modelisation of quality using the different variables.
An important part of the investigation relied on the relations of different variables related to the acidic composition of wine. We have found that in the sample of wine tested the different acid can be related. These relation between acids in wine made the use of more than 2 of these variables not significant to modelise quality. To continue the exploration, it could be interresting to modelise one of the acid variable using the other acid related variable as input.
The linear modelisation of the quality wasn’t of good quality. The relation between some of the variables and the non linear trend showed between quality and other variable didn’t help to find a good fit. Also the use of quality, a qualitative variable as a dummy output variable might also not be the best modelisation technic. We could try to use different clustering or modelisation technics. Also we probably need to reduce the number of dimension of this dataset to take into account the relation between variables found. Maybe some additionnal variables such as the soil type, soil composition or other compositions informations could help modelise more precisely the quality of wine. Another information is that the dataset is strongly unbalanced between the quality categories and that 80% of the wine falls into the medium quality categories. We have only a few wine sample for bad and good quality. The unbalanced characteristics of this dataset are also part of the difficulty to accurately modelise quality. With such dataset, the model could be overtrained to find medium quality wine.